288 citations · 1.7k across the 31 of their papers we have counts for
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math.MG2015★ 85 cited
Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves
Matthias Liero, Alexander Mielke, Giuseppe Savaré
We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance. The ne…
math.MG2011★ 288 cited
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study o…